Spline-interpolation solution of Cauchy problem for a harmonic function in a simply connected 3D domain

Document Type : Research Article

Authors

1 Lobachevskiy Institute of Mathematics and Mechanics, Kazan Federal University, Kremlevskaya st., 35, Kazan, 420008, Russia

2 Kazan National Research Technical University, K. Marksa st., 10, Kazan, 420111, Russia

Abstract

Here we construct an approximate spline-interpolation solution of the Cauchy problem for the Laplace equation. Our construction describes two different methods based on solution of integral equations. The first method involves singular integral equation, and the second one is based on solution of a Fredholm equation. We present the linear and the polynomial examples clarifying the construction approaches.

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References

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Journal of Mathematical Modeling
Volume 14, Issue 1
March 2026
Pages 315-325

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